DATA COMPRESSION AND ADAPTIVE HISTOGRAMS
Olivier Catoni · Foundations of Computational Mathematics · 2002
We describe and study in this paper a two step estimation scheme for density estimation from i.i.d. observations. Each step is based on the Gibbs aggregation rule and computes an adaptive histogram for which a non asymptotic oracle inequality is satised. The estimator computed in the first step is used to code the data in the unit interval in a way that is inspired by arithmetic coding. The second estimator analyzes the coded sample and refines the first one. Numerical evidences are provided of the efficiency of the method.